2.2. THEPHOTOELECTRICEFFECT 25
whatissurprisingaboutitisthattheenergyoftheemittedelectronsisindependent
oftheintensityoftheincidentlight.
Theexperimentalsetup,usedtomeasuretheenergyofthemostenergeticelec-
trons, isshowninFig. [2.2]. Theelectronsareemittedatthe photocathode,fall
onacollectingplate,andcompleteacircuit. Theresultingcurrentismeasuredby
anammeter. AbatterycanbeusedtoputapotentialdifferenceV acrossthegap
betweenthecathodeandtheplate,whichtendstorepeltheelectronsbacktowards
thecathode.Foranelectrontoreachthecollectingplate,itmusthaveanenergyof
atleasteV,whereeisthemagnitudeofthechargeofanelectron. Astherepelling
potentialisincreased,fewerelectronshavesufficientenergytoreachtheplate,and
thecurrentmeasuredbytheammeterdecreases. LetVs denotethevoltagewhere
thecurrentjustvanishes;i.e. Vsisthelowestvoltagesuchthat,atanyV >Vs,the
currentiszero. Thismeansthatthemaximumenergyoftheemittedelectronsisjust
Emax=eVs (2.9)ItisfoundexperimentallythatEmax,contrarytoexpectation,isindependentof
theintensityofthelightfallingonthephotocathode. Astheintensityincreases,for
fixedlightfrequency,thenumberofemittedelectronsincreases,butEmaxisconstant.
Ontheotherhand,whenEmaxisplottedasafunctionoffrequency,theresultisas
showninFig. [2.3]. Forfrequenciesfgreaterthansomeminimumf 0 =E 0 /h,the
dataforEmaxvs.ffitsastraightline,whoseslopeequalsPlanck’sconstant!Inother
words
Emax=hf−E 0 (2.10)
Einstein’sexplanationofthisformulaisquitesimple:Lightiscomposedofparti-
clescalledphotons.Eachphotonhasanenergy
Ephoton=hf (2.11)Supposethattheminimumenergyrequiredtofreeanelectronfromthephotocathode
isE 0 ,andanelectronabsorbsenergyfromthelightbyabsorbingaphoton. Then
themaximumpossibleenergyforanemittedelectronistheenergyoftheabsorbed
photon,lesstheminimumenergyrequiredtofreetheelectronfromthemetal,i.e.
Emax=hf−E 0 (2.12)Raisingtheintensityofthelightsimplyincreasesthenumberofphotonshittingthe
metalpersecond,whichincreasesthenumberofemittedelectronspersecond. But
theenergyofeachelectronisdependentonlyontheenergyoftheabsorbedphoton,
andthisenergydependsonlyonfrequency.
Einstein’stheoryofthephotoncompositionoflightimmediatelyexplainsPlanck’s
conditionthat theenergyofelectromagneticradiationoffrequencyf, inabox, is
restrictedtothevalues
E=nhf (2.13)